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Duality Principles in Nonconvex Systems: Theory, Methods and Applications (Nonconvex Optimization and Its Applications) download epub

by David Yang Gao


Epub Book: 1898 kb. | Fb2 Book: 1143 kb.

non-convex dynamical systems

non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. A self-contained appendix provides some necessary background from elementary functional analysis.

Tri-Duality in Nonconvex Systems cle{Gao2000DualityPI, title {Duality Principles in Nonconvex . 7. Applications, Open Problems and Concluding Remarks.

Tri-Duality in Nonconvex Systems. 4. Multi-Duality and Classifications of General Systems. Part III: Duality in Canonical Systems. 5. Duality in Geometrically Linear Systems. 6. Duality in Finite Deformation Systems. cle{Gao2000DualityPI, title {Duality Principles in Nonconvex Systems: Theory, Methods and Applications}, author {David Yang Gao}, journal {Meccanica}, year {2000}, volume {38}, pages {477-478} }. David Yang Gao. Preface.

David Yang Gao. Date: 2000.

Foundations of Bilevel Programming (Nonconvex Optimization and Its Applications). Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics).

OPTIMIZATION AND ITS APPLICATIONS Volume 39) (Nonconvex Optimization and Its Applications). by David Yang Gao. Published December 1, 1999 by Springer.

Duality Principles in Nonconvex Systems - Theory, Methods and Applications (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 39) (Nonconvex Optimization and Its Applications). The governing equations of equilibrium in nonlinear systems are amazingly beautiful.

From traditional convex systems to general nonlinear systems, we will study, in this chapter, the generalized duality theory and analytic solutions for one-dimensional nonconvex variational problems with applications to phase transitions, post-bifurcation, nonsmooth elastoplasticity an. .

From traditional convex systems to general nonlinear systems, we will study, in this chapter, the generalized duality theory and analytic solutions for one-dimensional nonconvex variational problems with applications to phase transitions, post-bifurcation, nonsmooth elastoplasticity and nonconvex dynamical systems. Because of the nonconvexity, the nice simple symmetry in the governing equations is broken and the beautiful one-to-one global duality relation no longer exists. The solutions in these systems are usually not unique.

non-convex dynamical systems.

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Duality Principles in Nonconvex Systems David Yang Gao Springer 9780792361459 : Offers a comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including engineering, mathematical economics, management science, financial engineering, and social science. This contributed volume consists of selected contributions from the Advanced Training Programme on Nonconvex Optimization and Its Applications held at Banaras Hindu University in March 2009.

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Duality Principles in Nonconvex Systems: Theory, Methods and Applications (Nonconvex Optimization and Its Applications) download epub
Engineering
Author: David Yang Gao
ISBN: 0792361458
Category: Engineering & Transportation
Subcategory: Engineering
Language: English
Publisher: Springer; 2000 edition (January 31, 2000)
Pages: 454 pages